- Propositional logic: language, deduction system, semantics, soundness, completeness;
- First-order logic: syntax, semantics, soundness, completeness, compactness;
- Set theory: fundamental axioms, ordinals, cardinals, transfinite induction, axiom of choice, continuum hypothesis;
- Constructive mathematics: intuitionistic logic, computable functions, λ-calculi, propositions as types;
- Limiting results: Peano arithmetic, Gödel’s incompleteness theorems, natural incompleteness results, incompleteness and computability.
The slides of the course are available: select the right academic year
Here are some exercises on natural deduction. Although not of high quality, these are the videos from the 2016/17 course.
Results (academic year 2019/20)